Please do all the questiosn if possible, that would be very helpful and apprecaited! Question 4 Let C5 be a simple cycle of length 5 on the vertex set {1,2, 3,4, 5}and Let K4 be the complete graph on the vertex set {a, b, c, d}. Let G be the graphon vertex set {1,2,3, 4, 5, a, b, c, d} where the edges between numbered verticescome from C5, the edges between lettered vertices come from K4 and we take allpossible edges of the form xy where x is a number and y is a letter.Answer the following questions.1. What is the largest degree of a vertex? Give an example of a vertex whichhas the largest possible degree.2. What is the largest size of a clique? Give an example of the vertex set ofsuch a clique.3. What is the largest size of an independent set? Give an example of suchan independent set.4. What is the chromatic number? Give a coloring which witnesses the chro-matic number and prove that there is no proper coloring with a smallernumber of colors.

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Description: Please do all the questiosn if possible, that would be very helpful and apprecaited! Question 4 Let C5 be a simple cycle of length 5 on the vertex set {1,2, 3,4, 5}and Let K4 be the complete graph on the vertex set {a, b, c, d}. Let G be the graphon

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Question 4 Let C; be a simple cycle of length 5 on the vertex set {1,2, 3, 4, 5} and Let K4 be the complete graph on the vertex set {a, b, c, d}. Let G be the graph on vertex set {1,2,3, 4, 5, a, b, c, d} where the edges between numbered vertices come from C3, the edges between lettered vertices come from K4 and we take all possible edges of the form xy where x is a number and y is a letter. Answer the following questions.

Question 4 Let C; be a simple cycle of length 5 on the vertex set {1,2, 3, 4, 5} and Let K4 be the complete graph on the vertex set {a, b, c, d}. Let G be the graph on vertex set {1,2,3, 4, 5, a, b, c, d} where the edges between numbered vertices come from C3, the edges between lettered vertices come from K4 and we take all possible edges of the form xy where x is a number and y is a letter. Answer the following questions.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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